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With 72 percent of precincts reporting, Sanders led Clinton 60 to 39 percent.

Recent polls showed Sanders with a double-digit lead going into Tuesday's Democratic presidential primary. The question for many became whether Clinton could close the gap.

Before a raucous crowd at Concord High School, Sanders thanked his volunteers for helping propel him to victory. (Watch Sanders' speech.)

"Together, we have sent a message that will echo from Wall Street to Washington, from Maine to California," Sanders said. "And that is that the government of our great country belongs to all of the people and not just a handful of wealthy campaign contributors and their super PACs."

Sanders cited the possibly record-breaking turnout as helping him win the first-in-the-nation primary. He said Democrats will need to continue to be inspired to keep the White House in November.

"What happened here in New Hampshire in terms of an enthusiastic and aroused electorate, people who came out in large numbers -- that is what will happen all over this country," Sanders said. "And let us never forget. Democrats and progressives win when voter turnout is high. Republicans win when people are demoralized and voter turnout is low."

He also called on Democrats to unite around the eventual nominee, whoever that is.

"I also hope that we all remember -- and this is a message not just to our opponents but to those who support me as well -- that we will need to come together in a few months to unite this party and this nation, because the right wing Republicans we oppose must not be allowed to gain the presidency," Sanders said.

Sanders blamed Republican control of the White House for driving the country into "the worst economic downturn of since the 1930s." He said Republicans want to give tax breaks to billionaires and cut Social Security and veterans benefits.

He also criticized Republicans for not admitting the reality of climate change.

"No, we will not allow back into the White House a political party which is so beholden to the fossil fuel industry that they cannot even acknowledge the scientific reality of climate change, let alone do anything about it."

Speaking at Southern New Hampshire University, Clinton congratulated Sanders on his victory. She told a fired-up crowd that she was taking her campaign to the entire country. (Watch Clinton's speech.)

"And that is the fight we're taking to the country," Clinton said. "What is the best way to change people's lives so we can all grow together? Who is the best change-maker?"

Clinton repeated themes that had become prominent in the past few weeks of the New Hampshire campaign, when she sought to portray Sanders as calling for changes that would be impractical. She said she would be a president who could get things done.

"Here's what I promise," Clinton said. "I will work harder than anyone to actually make the changes that make your lives better."